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A FORMULA TO FIND A SERIAL KILLER

      Is it possible to create a formula to locate a serial killer? Yes, one man has done it. Mathematics looks for a pattern. Serial killers leave some pattern. From that pattern, we can make a formula.

     Serial killers strike some distance away from their residence, but not too far away.


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    We select a large area where the killer is supposed to be hiding and map it. We superimpose the map on a square grid. Each square can be located using x, y coordinates as shown in the figure. We select a particular square(shaded one) and we will find the probability that "the killer will be residing there" using a formula.

The formula is 

            The formula seems more threatening than a serial killer. Anyway, we will go step by step and understand the formula.

Pij-- represents the probability finding the killer at the location i, j (x,y coordinates). The answer ranges from 0 to 1.  higher the probability,  higher the chance of finding him at the given place.

     xi, yi are co-ordinates of the place for which we want to find the probability. xn,yn are the co-ordinates of the place where the nth crime took place. Here we assume that he has already committed several crimes. 

(xi-xn)+(yi-yn) = the distance of separation of the killer's "home" and the spot of nth crime.

    B-Buffer area, the area in which the crimes are said to occur. It is a little distance away from his home.

    The first and second parts of the formula perform a sort of "balancing act" expressing the fact that as you move away from the criminal's base, the probability of crimes first increases (as you move through the buffer zone) and then decreases.

     Rossmo chose the value f,g,B and s using solved past criminal cases.

    The formula is calculated for each crime of the killer and all the answers are summed up. Finally, it gives the probability for the criminals base at a particular place i,j (co-ordinates).

    Once the formula is used to calculate the probabilities pij of all of the little squares in the grid, it is easy to make a hot zone map. You just color the squares with the highest probabilities bright yellow, slightly smaller probabilities orange, then red, and so on. leaving the square with low probabilities uncolored.

    The hot zone, the yellow region in which the criminal's residence is located, to a very high probability. The police team can investigate men within a certain range of ages, who live in the hot zone, and use surveillance, and stealth tactics to obtain DNA evidence from the suspects' discarded cigarette buts, drinking straws, and the like, which can be matched with DNA from the crime scene investigations. Then, in all probability, they will solve the case within a few days.

    Hence mathematics can solve a murder case if it is used with ingenuity.        

      

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